Screening experiments fractional factorial

Having identified the critical outputs and their specifications, we must determine the critical inputs (item 3). A type of design of experiment (DOE), called a screening experiment (fractional factorial), can be used to efficiently sort through a large number of potential inputs to identify those that are critical. A case study is presented illustrating the use of screening experiments. 

Now suppose there are 16 factors to be screened. We would have to add 15 dummy factors and use the 2 " saturated fractional factorial design, but this would give an efficiency of only 17/32 = 53%. This is not very efficient. Most researchers would rather eliminate one of their original 16 factors to give only 15 factors. There is a saturated fractional factorial design that will allow these factors to be screened in only 16 experiments. 

Screening Experiments with 2 q Fractional Factorial Designs... 

The sparsity of effects principle (see Box and Meyer, 1986) makes resolution III and IV fractional factorial designs particularly effective for factor screening. This principle states that, when many factors are studied in a factorial experiment, the system tends to be dominated by the main effects of some of the factors and a relatively small number of two-factor interactions. Thus resolution IV designs with main effects clear of two-factor interactions are very effective as screening... 

In Section 5, we introduced the dyestuffs experiment to illustrate the methods for screening for dispersion effects in unreplicated fractional factorial experiments. Typically we anticipate that smaller experiments will be used for screening. So, in this section, we analyze two sets of 16 runs that are extracted from the dyestuffs experiment and which constitute fractional factorials more typical of the actual size of screening experiments. 

Supersaturated designs, and likewise grouping screening designs, provide very little information about the effects of the factors studied, unless they are followed up with further experiments. If it is possible to use a fractional factorial design... 

The mixture experiment counterpart to conventional screening/fractional factorial experimentation also is possible. So-called axial designs have been developed for the purpose of providing screening-type mixture data for use in rough evaluation of the relative effects of a large number of mixture components on a response variable. The same kind of sequential experimental strategy illustrated in the process improvement example is applicable in mixture contexts as well as contexts free of a constraint such as (5-15). 

For screening purposes two-level fractional factorial designs 32 or Plackett-Bunnan designs [33 J are used. These designs allow evaluating the influence of a relatively high number of factors with a small number of experiments. 

This can be avoided H factorial designs or fractional factorial designs are used for designing screening experiments. Such experimental designs, and some other types of designs which can be used for screening experiments, will be discussed in Chapters 5-8. 

The two-level factorial designs are the most convenient and efficient way of laying out a screening experiment if the number of experimental variables does not exceed four. With more than four variables, it is more convenient to use a fractional factorial design. These designs are discussed in the next chapter. 

Assume that a 2 fractional factorial screening experiment has been run with seven variables, and where the "extra" variables have been defined as 4 = 12,... 

Let us now have a look at general screening experiments with many variables. Assume that k variables (xj, X2,..., xJ have been studied by a fractional factorial design and that a response surface model with linear and cross-product interaction terms has been determined. 

After a fractional factorial design has been run with a view to screen the experimental variables some variable may turn out to be insignificant. In such cases, the experiments which have been run can be used to obtain more detailed information on the remaining variables if the insignificant variable is left out. It is possible to consider the experiments already performed as a larger fraction of design in the remaining variables. 

The moral of this is, that whenever there are any doubts as to the form of the model, it is always better to use a fractional factorial design for screening experiments. With fractional factorial designs, analysis of the confounding pattern may give clues to how the model should be refined. 

At the outset of an experimental study, the shape of the response surface is not known. A quadratic model will be necessary only if the response surface is curved. It was discussed in Chapters 5 and 6 how linear and second-order interaction models can be established from factorial and fractional factorial designs, and how such models might be useful in screening experiments. However, these models cannot describe the curvatures of the surface, and should there be indications of curvature, it would be convenient if a complementary set of experiments could be run by which an interaction model could be augmented with squared terms. 

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